This video is useful for students of BTech/BE/Engineering/ BSc/MSc Mathematics students. Also for students preparing IIT-JAM, GATE, CSIR-NET and other exams.

published:10 Jul 2016

views:404209

Now we leave the world of real analysis and explore abstract algebra, beginning with some beautiful structures called groups that will serve to unify mathematics as a whole.

published:29 Mar 2013

views:203932

The first in a series of 4 lectures on Lie groups and Lie algebras (with a particular focus on physics) given by Gang Xu, a PSI Fellow, at the 2014-2015 PSI. This lecture provides an introduction to the subject, going through the motivation and basic examples/properties.
If you're having trouble seeing the board at any point in the lectures, you can check out this pdf with snapshots of the board -- one shot for each change that occurs:
http://pirsa.org/pdf/loadpdf.php?pirsa_number=14080028
These are NOT my videos! All rights, credit, etc. go to the Perimeter Institute, which can be found at the website linked to below. All the videos come from, and can be downloaded from in various formats and from previous years, the Perimeter Institute (where these lectures took place) website:
http://perimeterscholars.org/501.html

It was a Bio 171 lecture... until the choir started singing, the podium was brought in, and bridal party started walking the aisles, then it was a wedding venue.
Some 54 students were involved with an elaborate, unannounced, lecture prank. The professor, and class, were not informed, asked, or in any other way tipped off to the wedding they were about to witness.
The objector was not hurt in the making of this lecture prank.
We picked ALL the rose petals up at the conclusion of his lecture.
This is the original copy... I am the copyright holder.
Note: we are not affiliated with the UM Patriots, nor any other formal prank group. We operate independent from said groups, and are not a group of our own, merely a rag-tag group of friends. The why = just for the heck of it.
We had no idea what the lecture topic for that day was going to be... it was out of shear logistical feasibility and convenience that we chose said day to pull the prank.
Enjoy,
The Director
for licensing/usage please contact licensing@jukinmedia.com

published:17 Nov 2012

views:697097

VisualGroup Theory, Lecture 1.1: What is a group?
In this lecture, we will introduce the concept of a group using the famous Rubik's cube. The formal definition will be given later, in Lecture 1.5. For now, we just want to provide the intuition.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

VisualGroup Theory, Lecture 4.1: Homomorphisms and isomorphisms
A homomoprhism is function f between groups with the key property that f(ab)=f(a)f(b) holds for all elements, and an isomorphism is a bijective homomorphism. In this lecture, we use examples, Cayley diagrams, and multiplication tables to understand why this condition means that homomorphism are "structure preserving" maps. Along the way, we see some new groups, such as the roots of unity, and groups of matrices, that end up being isomorphic to groups that we familiar with.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

published:18 Mar 2016

views:5265

VisualGroup Theory, Lecture 7.1: Basic ring theory
A ring is an abelian group (R,+) with a second binary operation, multiplication and the distributive law. Multiplication need not commute, nor need there be multiplicative inverses, so a ring is like a field but without these properties. Rings attempt to generalize familiar algebraic structure like the integers, reals, or complex numbers. However, many unusual things can arise: the product of nonzero elements can be zero, and ax=ay need not imply that x=y. However, these unusal properties don't happen in "integral domains", which are essentially fields without multiplicative inverses. We see a number of examples of rings, including Z, Q, R, C, Z_n, matrix rings, the Hamiltonians, and group rings.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

One of the most important mathematical achievements of the 20th century was the collaborative effort, taking up more than 10,000 journal pages and mostly published between 1960 and 1980, that culminated in a complete classification of finite simple groups.

Interpretation

Three men appear to invade a small, cramped room, where they terrorize the scene. To the left, a man is hung by one of the intruders, and his arm twisted by another. A woman, seemingly the man's wife, is bound to one of the room's supports after having been raped. To the right, the child is about to be taken away by one of the intruders—note the feet near the top right hand corner.

Techniques

The subject matter is instantly chaotic, amplified by the artist's use of color and form. The painting is limited only to brown tones and vibrant red shades. Also, Beckmann mastered a form commonly associated with early 20th-century Fauvism artists such as Henri Matisse: the painting is compositionally flat and stilted, with no implementations of depth. For instance, though the woman appears at the forefront of the piece, she is bound to the room's back entrance. The artist deviated from conventional avant-garde, non-representational paintings such as Cubism and Dada. The sporadic interruptions of vibrant red and the painting's intrusive angularity serve to shock the viewer, and animate the scene with chaos and energy.

The Night (Disturbed song)

"The Night" is a song by the American heavy metal band Disturbed, the song is released as the fourth single from their fourth studio album, Indestructible. The song was the first from Indestructible to be completed musically. It is lyrically meant to portray the night as a living entity. Musically, the song is dark and textural. Disturbed guitarist Dan Donegan was almost universally praised for his work on this song, specifically during the guitar solo. A music video to correspond with the song was filmed in January 2009 and later released in late March 2009.

Recording and production

"The Night" was the first song from Indestructible to be completed musically. Disturbed vocalist David Draiman composed the vocal melody line for the song in just three days. Draiman later explained, "The instrumentation was so cool and so dark and textural that I right away kind of jumped into it." This caused Draiman to tentatively call the record The Night.

Musical style and lyrical themes

Perimeter Institute for Theoretical Physics

Perimeter Institute for Theoretical Physics (PI) is an independent research centre in foundational theoretical physics located in Waterloo, Ontario, Canada. It was founded in 1999. The Institute's founding and major benefactor is Canadian entrepreneur and philanthropist Mike Lazaridis.

In addition to research, Perimeter also provides scientific training and educational outreach activities to the general public. This is done in part through Perimeter’s Educational Outreach team.

History

Lazaridis' initial donation of $100 million was announced on October 23, 2000. A subsequent personal donation of $50 million was made on June 4, 2008.

Research operations began in 2001. Along with its research activities, Perimeter Institute operates an international outreach program. It hosts the International Summer School for Young Physicists every summer, which is a physics camp for high school students.

Under the stewardship of Howard Burton, the Institute's first Executive Director, PI initially operated out of Waterloo's historic post office on King Street. In October 2004, it moved into its custom-built facility on Caroline Street, across Silver Lake from Waterloo Park. The building was designed by Montreal architect firm Saucier + Perrotte, which received a Governor General's Medal for Architecture for the design in May 2006. The building next to PI, housing the Canadian Clay and Glass Gallery, won the same award for its architects in 1997. Perimeter Institute's building features an open glass facade along the north and west sides, contrasting with the slate-black metal walls of much of the rest of the building. Each researcher's office, as well as various lounge areas, features a full-wall blackboard for working out and theorizing in solo or group efforts.

Plot

UN agents Mike Graham (Brosnan) and Sabrina Carver (Alexandra Paul) are sent by their director Nick Caldwell to investigate the theft of Rembrandt's painting, The Night Watch. The trail takes them from Amsterdam initially to Hong Kong and involves them in not only art theft and forgery, but in the more serious high-tech schemes of Martin Schraeder and his bald North Korean cohort Mao Yixin.

This video is useful for students of BTech/BE/Engineering/ BSc/MSc Mathematics students. Also for students preparing IIT-JAM, GATE, CSIR-NET and other exams.

31:59

Introduction to Higher Mathematics - Lecture 16: Group Theory

Introduction to Higher Mathematics - Lecture 16: Group Theory

Introduction to Higher Mathematics - Lecture 16: Group Theory

Now we leave the world of real analysis and explore abstract algebra, beginning with some beautiful structures called groups that will serve to unify mathematics as a whole.

1:12:02

Lie Groups and Lie Algebras | Lecture 1

Lie Groups and Lie Algebras | Lecture 1

Lie Groups and Lie Algebras | Lecture 1

The first in a series of 4 lectures on Lie groups and Lie algebras (with a particular focus on physics) given by Gang Xu, a PSI Fellow, at the 2014-2015 PSI. This lecture provides an introduction to the subject, going through the motivation and basic examples/properties.
If you're having trouble seeing the board at any point in the lectures, you can check out this pdf with snapshots of the board -- one shot for each change that occurs:
http://pirsa.org/pdf/loadpdf.php?pirsa_number=14080028
These are NOT my videos! All rights, credit, etc. go to the Perimeter Institute, which can be found at the website linked to below. All the videos come from, and can be downloaded from in various formats and from previous years, the Perimeter Institute (where these lectures took place) website:
http://perimeterscholars.org/501.html

Wedding Interrupts Lecture (A Cappella Group) University of Michigan

It was a Bio 171 lecture... until the choir started singing, the podium was brought in, and bridal party started walking the aisles, then it was a wedding venue.
Some 54 students were involved with an elaborate, unannounced, lecture prank. The professor, and class, were not informed, asked, or in any other way tipped off to the wedding they were about to witness.
The objector was not hurt in the making of this lecture prank.
We picked ALL the rose petals up at the conclusion of his lecture.
This is the original copy... I am the copyright holder.
Note: we are not affiliated with the UM Patriots, nor any other formal prank group. We operate independent from said groups, and are not a group of our own, merely a rag-tag group of friends. The why = just for the heck of it.
We had no idea what the lecture topic for that day was going to be... it was out of shear logistical feasibility and convenience that we chose said day to pull the prank.
Enjoy,
The Director
for licensing/usage please contact licensing@jukinmedia.com

16:15

Visual Group Theory, Lecture 1.1: What is a group?

Visual Group Theory, Lecture 1.1: What is a group?

Visual Group Theory, Lecture 1.1: What is a group?

VisualGroup Theory, Lecture 1.1: What is a group?
In this lecture, we will introduce the concept of a group using the famous Rubik's cube. The formal definition will be given later, in Lecture 1.5. For now, we just want to provide the intuition.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

1:07:43

Lecture 4: The Night Watch: Rembrandt, Group Portraiture, and Dutch History

Lecture 4: The Night Watch: Rembrandt, Group Portraiture, and Dutch History

Lecture 4: The Night Watch: Rembrandt, Group Portraiture, and Dutch History

Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms

VisualGroup Theory, Lecture 4.1: Homomorphisms and isomorphisms
A homomoprhism is function f between groups with the key property that f(ab)=f(a)f(b) holds for all elements, and an isomorphism is a bijective homomorphism. In this lecture, we use examples, Cayley diagrams, and multiplication tables to understand why this condition means that homomorphism are "structure preserving" maps. Along the way, we see some new groups, such as the roots of unity, and groups of matrices, that end up being isomorphic to groups that we familiar with.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

32:36

Visual Group Theory, Lecture 7.1: Basic ring theory

Visual Group Theory, Lecture 7.1: Basic ring theory

Visual Group Theory, Lecture 7.1: Basic ring theory

VisualGroup Theory, Lecture 7.1: Basic ring theory
A ring is an abelian group (R,+) with a second binary operation, multiplication and the distributive law. Multiplication need not commute, nor need there be multiplicative inverses, so a ring is like a field but without these properties. Rings attempt to generalize familiar algebraic structure like the integers, reals, or complex numbers. However, many unusual things can arise: the product of nonzero elements can be zero, and ax=ay need not imply that x=y. However, these unusal properties don't happen in "integral domains", which are essentially fields without multiplicative inverses. We see a number of examples of rings, including Z, Q, R, C, Z_n, matrix rings, the Hamiltonians, and group rings.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

38:20

Visual Group Theory, Lecture 6.3: Polynomials and irreducibility

Visual Group Theory, Lecture 6.3: Polynomials and irreducibility

Visual Group Theory, Lecture 6.3: Polynomials and irreducibility

VisualGroup Theory, Lecture 6.3: Polynomials and irreducibility
A complex number is algebraic over Q (the rationals) if it is the root of a polynomial with rational coefficients. It is clear that every number that can be written with arithmetic and radicals is rational. Galois' big achievement was proving that the converse fails. In fact, there are roots of degree-5 polynomials that cannot be expressed using radicals, which means that there cannot exist a formula for the quintic. Next, we turn to the question of when a polynomial is irreducible over Q, which means that it cannot be factored into a product of two lower-degree polynomials. Though there is no one sure-fire method to answer this, a technique called Eisenstein's criterion works for many polynomials. We conclude by looking at extensions of Q, and define the minimal polynomial of an algebraic number r to be the (unique) monic irreducible polynomial for which f(r)=0. It turns out that the degree of this "minimal polynomial" is equal to the dimension of the extension field Q(r) over Q.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

18:12

Visual Group Theory, Lecture 1.4: Group presentations

Visual Group Theory, Lecture 1.4: Group presentations

Visual Group Theory, Lecture 1.4: Group presentations

VisualGroup Theory, Lecture 1.4: Group presentations
We begin this lecture by learning how to take a Cayley diagram and label its nodes with the elements of a group. Such a labeled diagram can function as a "group calculator". It leads to the notion of a "group presentation", which is a convenient way to describe a group by listing a generating set, and a collection of relations that they generators satisfy.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

1:17:44

Lie Groups and Lie Algebras | Lecture 2

Lie Groups and Lie Algebras | Lecture 2

Lie Groups and Lie Algebras | Lecture 2

The second in a series of 4 lectures on Lie groups and Lie algebras (with a particular focus on physics) given by Gang Xu, a PSI Fellow, at the 2014-2015 PSI. This lecture covers groups, group representations, structure constants, and the Poincare group.
If you're having trouble seeing the board at any point in the lectures, you can check out this pdf with snapshots of the board -- one shot for each change that occurs:
http://pirsa.org/pdf/loadpdf.php?pirsa_number=14080029
These are NOT my videos! All rights, credit, etc. go to the Perimeter Institute, which can be found at the website linked to below. All the videos come from, and can be downloaded from in various formats and from previous years, the Perimeter Institute (where these lectures took place) website:
http://perimeterscholars.org/501.html

This video is useful for students of BTech/BE/Engineering/ BSc/MSc Mathematics students. Also for students preparing IIT-JAM, GATE, CSIR-NET and other exams.

published: 10 Jul 2016

Introduction to Higher Mathematics - Lecture 16: Group Theory

Now we leave the world of real analysis and explore abstract algebra, beginning with some beautiful structures called groups that will serve to unify mathematics as a whole.

published: 29 Mar 2013

Lie Groups and Lie Algebras | Lecture 1

The first in a series of 4 lectures on Lie groups and Lie algebras (with a particular focus on physics) given by Gang Xu, a PSI Fellow, at the 2014-2015 PSI. This lecture provides an introduction to the subject, going through the motivation and basic examples/properties.
If you're having trouble seeing the board at any point in the lectures, you can check out this pdf with snapshots of the board -- one shot for each change that occurs:
http://pirsa.org/pdf/loadpdf.php?pirsa_number=14080028
These are NOT my videos! All rights, credit, etc. go to the Perimeter Institute, which can be found at the website linked to below. All the videos come from, and can be downloaded from in various formats and from previous years, the Perimeter Institute (where these lectures took place) website:
http:...

Teaching in Large Group Lecture Classes

Wedding Interrupts Lecture (A Cappella Group) University of Michigan

It was a Bio 171 lecture... until the choir started singing, the podium was brought in, and bridal party started walking the aisles, then it was a wedding venue.
Some 54 students were involved with an elaborate, unannounced, lecture prank. The professor, and class, were not informed, asked, or in any other way tipped off to the wedding they were about to witness.
The objector was not hurt in the making of this lecture prank.
We picked ALL the rose petals up at the conclusion of his lecture.
This is the original copy... I am the copyright holder.
Note: we are not affiliated with the UM Patriots, nor any other formal prank group. We operate independent from said groups, and are not a group of our own, merely a rag-tag group of friends. The why = just for the heck of it.
We had no idea ...

published: 17 Nov 2012

Visual Group Theory, Lecture 1.1: What is a group?

VisualGroup Theory, Lecture 1.1: What is a group?
In this lecture, we will introduce the concept of a group using the famous Rubik's cube. The formal definition will be given later, in Lecture 1.5. For now, we just want to provide the intuition.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

published: 24 Feb 2016

Lecture 4: The Night Watch: Rembrandt, Group Portraiture, and Dutch History

Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms

VisualGroup Theory, Lecture 4.1: Homomorphisms and isomorphisms
A homomoprhism is function f between groups with the key property that f(ab)=f(a)f(b) holds for all elements, and an isomorphism is a bijective homomorphism. In this lecture, we use examples, Cayley diagrams, and multiplication tables to understand why this condition means that homomorphism are "structure preserving" maps. Along the way, we see some new groups, such as the roots of unity, and groups of matrices, that end up being isomorphic to groups that we familiar with.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

published: 18 Mar 2016

Visual Group Theory, Lecture 7.1: Basic ring theory

VisualGroup Theory, Lecture 7.1: Basic ring theory
A ring is an abelian group (R,+) with a second binary operation, multiplication and the distributive law. Multiplication need not commute, nor need there be multiplicative inverses, so a ring is like a field but without these properties. Rings attempt to generalize familiar algebraic structure like the integers, reals, or complex numbers. However, many unusual things can arise: the product of nonzero elements can be zero, and ax=ay need not imply that x=y. However, these unusal properties don't happen in "integral domains", which are essentially fields without multiplicative inverses. We see a number of examples of rings, including Z, Q, R, C, Z_n, matrix rings, the Hamiltonians, and group rings.
Course webpage (with lecture notes, HW...

published: 02 May 2016

Visual Group Theory, Lecture 6.3: Polynomials and irreducibility

VisualGroup Theory, Lecture 6.3: Polynomials and irreducibility
A complex number is algebraic over Q (the rationals) if it is the root of a polynomial with rational coefficients. It is clear that every number that can be written with arithmetic and radicals is rational. Galois' big achievement was proving that the converse fails. In fact, there are roots of degree-5 polynomials that cannot be expressed using radicals, which means that there cannot exist a formula for the quintic. Next, we turn to the question of when a polynomial is irreducible over Q, which means that it cannot be factored into a product of two lower-degree polynomials. Though there is no one sure-fire method to answer this, a technique called Eisenstein's criterion works for many polynomials. We conclude by looking at ...

published: 09 Apr 2016

Visual Group Theory, Lecture 1.4: Group presentations

VisualGroup Theory, Lecture 1.4: Group presentations
We begin this lecture by learning how to take a Cayley diagram and label its nodes with the elements of a group. Such a labeled diagram can function as a "group calculator". It leads to the notion of a "group presentation", which is a convenient way to describe a group by listing a generating set, and a collection of relations that they generators satisfy.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

published: 24 Feb 2016

Lie Groups and Lie Algebras | Lecture 2

The second in a series of 4 lectures on Lie groups and Lie algebras (with a particular focus on physics) given by Gang Xu, a PSI Fellow, at the 2014-2015 PSI. This lecture covers groups, group representations, structure constants, and the Poincare group.
If you're having trouble seeing the board at any point in the lectures, you can check out this pdf with snapshots of the board -- one shot for each change that occurs:
http://pirsa.org/pdf/loadpdf.php?pirsa_number=14080029
These are NOT my videos! All rights, credit, etc. go to the Perimeter Institute, which can be found at the website linked to below. All the videos come from, and can be downloaded from in various formats and from previous years, the Perimeter Institute (where these lectures took place) website:
http://perimeterschola...

Lie Groups and Lie Algebras | Lecture 1

The first in a series of 4 lectures on Lie groups and Lie algebras (with a particular focus on physics) given by Gang Xu, a PSI Fellow, at the 2014-2015 PSI. Th...

The first in a series of 4 lectures on Lie groups and Lie algebras (with a particular focus on physics) given by Gang Xu, a PSI Fellow, at the 2014-2015 PSI. This lecture provides an introduction to the subject, going through the motivation and basic examples/properties.
If you're having trouble seeing the board at any point in the lectures, you can check out this pdf with snapshots of the board -- one shot for each change that occurs:
http://pirsa.org/pdf/loadpdf.php?pirsa_number=14080028
These are NOT my videos! All rights, credit, etc. go to the Perimeter Institute, which can be found at the website linked to below. All the videos come from, and can be downloaded from in various formats and from previous years, the Perimeter Institute (where these lectures took place) website:
http://perimeterscholars.org/501.html

The first in a series of 4 lectures on Lie groups and Lie algebras (with a particular focus on physics) given by Gang Xu, a PSI Fellow, at the 2014-2015 PSI. This lecture provides an introduction to the subject, going through the motivation and basic examples/properties.
If you're having trouble seeing the board at any point in the lectures, you can check out this pdf with snapshots of the board -- one shot for each change that occurs:
http://pirsa.org/pdf/loadpdf.php?pirsa_number=14080028
These are NOT my videos! All rights, credit, etc. go to the Perimeter Institute, which can be found at the website linked to below. All the videos come from, and can be downloaded from in various formats and from previous years, the Perimeter Institute (where these lectures took place) website:
http://perimeterscholars.org/501.html

Wedding Interrupts Lecture (A Cappella Group) University of Michigan

It was a Bio 171 lecture... until the choir started singing, the podium was brought in, and bridal party started walking the aisles, then it was a wedding venue...

It was a Bio 171 lecture... until the choir started singing, the podium was brought in, and bridal party started walking the aisles, then it was a wedding venue.
Some 54 students were involved with an elaborate, unannounced, lecture prank. The professor, and class, were not informed, asked, or in any other way tipped off to the wedding they were about to witness.
The objector was not hurt in the making of this lecture prank.
We picked ALL the rose petals up at the conclusion of his lecture.
This is the original copy... I am the copyright holder.
Note: we are not affiliated with the UM Patriots, nor any other formal prank group. We operate independent from said groups, and are not a group of our own, merely a rag-tag group of friends. The why = just for the heck of it.
We had no idea what the lecture topic for that day was going to be... it was out of shear logistical feasibility and convenience that we chose said day to pull the prank.
Enjoy,
The Director
for licensing/usage please contact licensing@jukinmedia.com

It was a Bio 171 lecture... until the choir started singing, the podium was brought in, and bridal party started walking the aisles, then it was a wedding venue.
Some 54 students were involved with an elaborate, unannounced, lecture prank. The professor, and class, were not informed, asked, or in any other way tipped off to the wedding they were about to witness.
The objector was not hurt in the making of this lecture prank.
We picked ALL the rose petals up at the conclusion of his lecture.
This is the original copy... I am the copyright holder.
Note: we are not affiliated with the UM Patriots, nor any other formal prank group. We operate independent from said groups, and are not a group of our own, merely a rag-tag group of friends. The why = just for the heck of it.
We had no idea what the lecture topic for that day was going to be... it was out of shear logistical feasibility and convenience that we chose said day to pull the prank.
Enjoy,
The Director
for licensing/usage please contact licensing@jukinmedia.com

VisualGroup Theory, Lecture 1.1: What is a group?
In this lecture, we will introduce the concept of a group using the famous Rubik's cube. The formal definition will be given later, in Lecture 1.5. For now, we just want to provide the intuition.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

VisualGroup Theory, Lecture 1.1: What is a group?
In this lecture, we will introduce the concept of a group using the famous Rubik's cube. The formal definition will be given later, in Lecture 1.5. For now, we just want to provide the intuition.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms

VisualGroup Theory, Lecture 4.1: Homomorphisms and isomorphisms
A homomoprhism is function f between groups with the key property that f(ab)=f(a)f(b) holds fo...

VisualGroup Theory, Lecture 4.1: Homomorphisms and isomorphisms
A homomoprhism is function f between groups with the key property that f(ab)=f(a)f(b) holds for all elements, and an isomorphism is a bijective homomorphism. In this lecture, we use examples, Cayley diagrams, and multiplication tables to understand why this condition means that homomorphism are "structure preserving" maps. Along the way, we see some new groups, such as the roots of unity, and groups of matrices, that end up being isomorphic to groups that we familiar with.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

VisualGroup Theory, Lecture 4.1: Homomorphisms and isomorphisms
A homomoprhism is function f between groups with the key property that f(ab)=f(a)f(b) holds for all elements, and an isomorphism is a bijective homomorphism. In this lecture, we use examples, Cayley diagrams, and multiplication tables to understand why this condition means that homomorphism are "structure preserving" maps. Along the way, we see some new groups, such as the roots of unity, and groups of matrices, that end up being isomorphic to groups that we familiar with.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

VisualGroup Theory, Lecture 7.1: Basic ring theory
A ring is an abelian group (R,+) with a second binary operation, multiplication and the distributive law. Multiplication need not commute, nor need there be multiplicative inverses, so a ring is like a field but without these properties. Rings attempt to generalize familiar algebraic structure like the integers, reals, or complex numbers. However, many unusual things can arise: the product of nonzero elements can be zero, and ax=ay need not imply that x=y. However, these unusal properties don't happen in "integral domains", which are essentially fields without multiplicative inverses. We see a number of examples of rings, including Z, Q, R, C, Z_n, matrix rings, the Hamiltonians, and group rings.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

VisualGroup Theory, Lecture 7.1: Basic ring theory
A ring is an abelian group (R,+) with a second binary operation, multiplication and the distributive law. Multiplication need not commute, nor need there be multiplicative inverses, so a ring is like a field but without these properties. Rings attempt to generalize familiar algebraic structure like the integers, reals, or complex numbers. However, many unusual things can arise: the product of nonzero elements can be zero, and ax=ay need not imply that x=y. However, these unusal properties don't happen in "integral domains", which are essentially fields without multiplicative inverses. We see a number of examples of rings, including Z, Q, R, C, Z_n, matrix rings, the Hamiltonians, and group rings.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

Visual Group Theory, Lecture 6.3: Polynomials and irreducibility

VisualGroup Theory, Lecture 6.3: Polynomials and irreducibility
A complex number is algebraic over Q (the rationals) if it is the root of a polynomial with ra...

VisualGroup Theory, Lecture 6.3: Polynomials and irreducibility
A complex number is algebraic over Q (the rationals) if it is the root of a polynomial with rational coefficients. It is clear that every number that can be written with arithmetic and radicals is rational. Galois' big achievement was proving that the converse fails. In fact, there are roots of degree-5 polynomials that cannot be expressed using radicals, which means that there cannot exist a formula for the quintic. Next, we turn to the question of when a polynomial is irreducible over Q, which means that it cannot be factored into a product of two lower-degree polynomials. Though there is no one sure-fire method to answer this, a technique called Eisenstein's criterion works for many polynomials. We conclude by looking at extensions of Q, and define the minimal polynomial of an algebraic number r to be the (unique) monic irreducible polynomial for which f(r)=0. It turns out that the degree of this "minimal polynomial" is equal to the dimension of the extension field Q(r) over Q.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

VisualGroup Theory, Lecture 6.3: Polynomials and irreducibility
A complex number is algebraic over Q (the rationals) if it is the root of a polynomial with rational coefficients. It is clear that every number that can be written with arithmetic and radicals is rational. Galois' big achievement was proving that the converse fails. In fact, there are roots of degree-5 polynomials that cannot be expressed using radicals, which means that there cannot exist a formula for the quintic. Next, we turn to the question of when a polynomial is irreducible over Q, which means that it cannot be factored into a product of two lower-degree polynomials. Though there is no one sure-fire method to answer this, a technique called Eisenstein's criterion works for many polynomials. We conclude by looking at extensions of Q, and define the minimal polynomial of an algebraic number r to be the (unique) monic irreducible polynomial for which f(r)=0. It turns out that the degree of this "minimal polynomial" is equal to the dimension of the extension field Q(r) over Q.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

VisualGroup Theory, Lecture 1.4: Group presentations
We begin this lecture by learning how to take a Cayley diagram and label its nodes with the elements of a group. Such a labeled diagram can function as a "group calculator". It leads to the notion of a "group presentation", which is a convenient way to describe a group by listing a generating set, and a collection of relations that they generators satisfy.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

VisualGroup Theory, Lecture 1.4: Group presentations
We begin this lecture by learning how to take a Cayley diagram and label its nodes with the elements of a group. Such a labeled diagram can function as a "group calculator". It leads to the notion of a "group presentation", which is a convenient way to describe a group by listing a generating set, and a collection of relations that they generators satisfy.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

Lie Groups and Lie Algebras | Lecture 2

The second in a series of 4 lectures on Lie groups and Lie algebras (with a particular focus on physics) given by Gang Xu, a PSI Fellow, at the 2014-2015 PSI. T...

The second in a series of 4 lectures on Lie groups and Lie algebras (with a particular focus on physics) given by Gang Xu, a PSI Fellow, at the 2014-2015 PSI. This lecture covers groups, group representations, structure constants, and the Poincare group.
If you're having trouble seeing the board at any point in the lectures, you can check out this pdf with snapshots of the board -- one shot for each change that occurs:
http://pirsa.org/pdf/loadpdf.php?pirsa_number=14080029
These are NOT my videos! All rights, credit, etc. go to the Perimeter Institute, which can be found at the website linked to below. All the videos come from, and can be downloaded from in various formats and from previous years, the Perimeter Institute (where these lectures took place) website:
http://perimeterscholars.org/501.html

The second in a series of 4 lectures on Lie groups and Lie algebras (with a particular focus on physics) given by Gang Xu, a PSI Fellow, at the 2014-2015 PSI. This lecture covers groups, group representations, structure constants, and the Poincare group.
If you're having trouble seeing the board at any point in the lectures, you can check out this pdf with snapshots of the board -- one shot for each change that occurs:
http://pirsa.org/pdf/loadpdf.php?pirsa_number=14080029
These are NOT my videos! All rights, credit, etc. go to the Perimeter Institute, which can be found at the website linked to below. All the videos come from, and can be downloaded from in various formats and from previous years, the Perimeter Institute (where these lectures took place) website:
http://perimeterscholars.org/501.html

Lie Groups and Lie Algebras | Lecture 1

The first in a series of 4 lectures on Lie groups and Lie algebras (with a particular focus on physics) given by Gang Xu, a PSI Fellow, at the 2014-2015 PSI. This lecture provides an introduction to the subject, going through the motivation and basic examples/properties.
If you're having trouble seeing the board at any point in the lectures, you can check out this pdf with snapshots of the board -- one shot for each change that occurs:
http://pirsa.org/pdf/loadpdf.php?pirsa_number=14080028
These are NOT my videos! All rights, credit, etc. go to the Perimeter Institute, which can be found at the website linked to below. All the videos come from, and can be downloaded from in various formats and from previous years, the Perimeter Institute (where these lectures took place) website:
http://perimeterscholars.org/501.html

Wedding Interrupts Lecture (A Cappella Group) University of Michigan

It was a Bio 171 lecture... until the choir started singing, the podium was brought in, and bridal party started walking the aisles, then it was a wedding venue.
Some 54 students were involved with an elaborate, unannounced, lecture prank. The professor, and class, were not informed, asked, or in any other way tipped off to the wedding they were about to witness.
The objector was not hurt in the making of this lecture prank.
We picked ALL the rose petals up at the conclusion of his lecture.
This is the original copy... I am the copyright holder.
Note: we are not affiliated with the UM Patriots, nor any other formal prank group. We operate independent from said groups, and are not a group of our own, merely a rag-tag group of friends. The why = just for the heck of it.
We had no idea what the lecture topic for that day was going to be... it was out of shear logistical feasibility and convenience that we chose said day to pull the prank.
Enjoy,
The Director
for licensing/usage please contact licensing@jukinmedia.com

Visual Group Theory, Lecture 1.1: What is a group?

VisualGroup Theory, Lecture 1.1: What is a group?
In this lecture, we will introduce the concept of a group using the famous Rubik's cube. The formal definition will be given later, in Lecture 1.5. For now, we just want to provide the intuition.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms

VisualGroup Theory, Lecture 4.1: Homomorphisms and isomorphisms
A homomoprhism is function f between groups with the key property that f(ab)=f(a)f(b) holds for all elements, and an isomorphism is a bijective homomorphism. In this lecture, we use examples, Cayley diagrams, and multiplication tables to understand why this condition means that homomorphism are "structure preserving" maps. Along the way, we see some new groups, such as the roots of unity, and groups of matrices, that end up being isomorphic to groups that we familiar with.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

Visual Group Theory, Lecture 7.1: Basic ring theory

VisualGroup Theory, Lecture 7.1: Basic ring theory
A ring is an abelian group (R,+) with a second binary operation, multiplication and the distributive law. Multiplication need not commute, nor need there be multiplicative inverses, so a ring is like a field but without these properties. Rings attempt to generalize familiar algebraic structure like the integers, reals, or complex numbers. However, many unusual things can arise: the product of nonzero elements can be zero, and ax=ay need not imply that x=y. However, these unusal properties don't happen in "integral domains", which are essentially fields without multiplicative inverses. We see a number of examples of rings, including Z, Q, R, C, Z_n, matrix rings, the Hamiltonians, and group rings.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

Visual Group Theory, Lecture 6.3: Polynomials and irreducibility

VisualGroup Theory, Lecture 6.3: Polynomials and irreducibility
A complex number is algebraic over Q (the rationals) if it is the root of a polynomial with rational coefficients. It is clear that every number that can be written with arithmetic and radicals is rational. Galois' big achievement was proving that the converse fails. In fact, there are roots of degree-5 polynomials that cannot be expressed using radicals, which means that there cannot exist a formula for the quintic. Next, we turn to the question of when a polynomial is irreducible over Q, which means that it cannot be factored into a product of two lower-degree polynomials. Though there is no one sure-fire method to answer this, a technique called Eisenstein's criterion works for many polynomials. We conclude by looking at extensions of Q, and define the minimal polynomial of an algebraic number r to be the (unique) monic irreducible polynomial for which f(r)=0. It turns out that the degree of this "minimal polynomial" is equal to the dimension of the extension field Q(r) over Q.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

Visual Group Theory, Lecture 1.4: Group presentations

VisualGroup Theory, Lecture 1.4: Group presentations
We begin this lecture by learning how to take a Cayley diagram and label its nodes with the elements of a group. Such a labeled diagram can function as a "group calculator". It leads to the notion of a "group presentation", which is a convenient way to describe a group by listing a generating set, and a collection of relations that they generators satisfy.
Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

One of the most important mathematical achievements of the 20th century was the collaborative effort, taking up more than 10,000 journal pages and mostly published between 1960 and 1980, that culminated in a complete classification of finite simple groups.

Three recent graduates of the elite Peking University have been taken away by authorities, the Jasic Workers SupportGroup said in a statement late Tuesday ... One fourth-year history student, writing on the Jasic Workers Support Group's website, said he was thrown to the ground outside of a lecture hall by five people dressed in black....

College of Businesslecturer Chandra Schwab, along with a group of volunteer international students, will host mini language lessons on Friday, Nov. 16, from 1 to 2 p.m. in the second floor auditorium of the Howard HawksHall... She received her bachelor's degree in social studies education at St ... news@dailynebraskan.com. // <![CDATA[ _ // ]]>. ....

Visual Group Theory, Lecture 1.4: Group presentati...

Lie Groups and Lie Algebras | Lecture 2...

Latest News for: group lecture

Three recent graduates of the elite Peking University have been taken away by authorities, the Jasic Workers SupportGroup said in a statement late Tuesday ... One fourth-year history student, writing on the Jasic Workers Support Group's website, said he was thrown to the ground outside of a lecture hall by five people dressed in black....

College of Businesslecturer Chandra Schwab, along with a group of volunteer international students, will host mini language lessons on Friday, Nov. 16, from 1 to 2 p.m. in the second floor auditorium of the Howard HawksHall... She received her bachelor's degree in social studies education at St ... news@dailynebraskan.com. // <![CDATA[ _ // ]]>. ....

The first thing Jannet Rodriguez heard Wednesday as she walked into John Waldron’s history class for the final time was that her favorite teacher had brought her a gift ... “He’ll do a lecture and group exercise with the freshmen, who are not easy to control, and he’s got them eating out of his hands just as the seniors do,” she said ... “Booker T ... Twitter....

Three recent graduates of the elite Peking University have been taken away by authorities, the Jasic Workers SupportGroup said in a statement late Tuesday ... One fourth-year history student, writing on the Jasic Workers Support Group's website, said he was thrown to the ground outside of a lecture hall by five people dressed in black....

Huntinglecture planned. COOPERSTOWN — Hunting and its role in wildlife management and conservation will be the topic of the next Be Informed LectureSeries at 6.30 p.m ... The Be Informed lecture series is a joint program of OCCA and MohicanFarm. Shepherds group to review 30 years....

... after-school programs, Scouts divisions or other groups ... Students from the "Choose Your Info" group, during the project, have given lectures for about 6 500 people all over the Czech Republic and in Slovakia, according to Kateřina Křivánková, a representative of the association....

Fairlee — Since its founding about a year ago, Fairlee Community Arts has brought concerts to the newly renovated auditorium in Fairlee Town Hall and hosted a successful summer concert series.This Thursday at 6.30 p.m., the group is expanding its offerings by sponsoring a lecture, “Vermont’s Histori... ....

DEAR ANNIE(R). BY ANNIE LANE ... In Ocala, Florida, there is a hospital-sponsored group called Prestige 55 ... A newer group in town has a similar set of lectures at noon, followed by free lunches ... Sometimes the pool group will sit together at a meal table ... And as you say, some newspapers periodically print lists of local clubs and volunteer service groups....

Known as the March of Independence, it has been organized annually by far-right groups to celebrate the restoration of the country's sovereignty in 1918. So while Macron, in Paris, was lecturingPresidentDonald Trump — who recently embraced nationalism — and other ......